.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/analytical/stoichiometry/plot_01_richter_stoichiometry.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_analytical_stoichiometry_plot_01_richter_stoichiometry.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_analytical_stoichiometry_plot_01_richter_stoichiometry.py:


Richter's stoichiometry: equivalent weights, balanced equations, limiting reagents
==================================================================================

Jeremias Richter, who coined the word *stoichiometry*, tabulated how many
parts by weight of each base neutralize a fixed weight of an acid, and
found the proportions were fixed and mutually consistent. Today those
numbers follow from a balanced equation and molar masses.
:func:`~chemistrykit.stoichiometry.balance_equation` finds the smallest
integer coefficients that conserve every element (and charge) as the
exact null space of the composition matrix. Left: Richter-style
neutralization equivalents, the grams of each base that neutralize
1000 g of sulfuric acid. Right: product yield as the N2:H2 feed ratio
varies. It rises while H2 is limiting and falls once N2 is, with the
kink at the stoichiometric 1:3 ratio
(:func:`~chemistrykit.stoichiometry.limiting_reagent`).

.. GENERATED FROM PYTHON SOURCE LINES 20-52

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.periodic_table import molar_mass
    from chemistrykit.stoichiometry import balance_equation, limiting_reagent, theoretical_yield

    for equation in ("C3H8 + O2 -> CO2 + H2O", "KMnO4 + HCl -> KCl + MnCl2 + H2O + Cl2", "MnO4- + Fe2+ + H+ -> Mn2+ + Fe3+ + H2O"):
        print(balance_equation(equation))

    bases = ["NaOH", "KOH", "Ca(OH)2", "Mg(OH)2", "NH3"]
    products = {"NaOH": "Na2SO4 + H2O", "KOH": "K2SO4 + H2O", "Ca(OH)2": "CaSO4 + H2O", "Mg(OH)2": "MgSO4 + H2O", "NH3": "(NH4)2SO4"}
    grams = []
    for base in bases:
        eq = balance_equation(f"H2SO4 + {base} -> {products[base]}")
        grams.append(1000.0 / molar_mass("H2SO4") / eq.reactants["H2SO4"] * eq.reactants[base] * molar_mass(base))

    fig, axes = plt.subplots(1, 2, figsize=(12, 4.8))
    axes[0].bar(bases, grams, color="steelblue")
    axes[0].set_ylabel("g of base per 1000 g H2SO4")
    axes[0].set_title("Neutralization equivalents, Richter-style")

    total = 4.0  # mol of N2 + H2 fed
    f_N2 = np.linspace(0.01, 0.99, 197)
    nh3 = [theoretical_yield("N2 + H2 -> NH3", {"N2": f * total, "H2": (1 - f) * total}, "NH3") for f in f_N2]
    axes[1].plot(f_N2, nh3, color="darkorange")
    axes[1].axvline(0.25, color="gray", linestyle="--", label="stoichiometric N2:H2 = 1:3")
    axes[1].set_xlabel("mole fraction of N2 in the feed")
    axes[1].set_ylabel("theoretical NH3 (mol)")
    axes[1].set_title("Yield is set by the limiting reagent")
    axes[1].legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/analytical/stoichiometry/images/sphx_glr_plot_01_richter_stoichiometry_001.png
   :alt: Neutralization equivalents, Richter-style, Yield is set by the limiting reagent
   :srcset: /api/gallery/analytical/stoichiometry/images/sphx_glr_plot_01_richter_stoichiometry_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    C3H8 + 5O2 -> 3CO2 + 4H2O
    2KMnO4 + 16HCl -> 2KCl + 2MnCl2 + 8H2O + 5Cl2
    MnO4- + 5Fe2+ + 8H+ -> Mn2+ + 5Fe3+ + 4H2O




.. GENERATED FROM PYTHON SOURCE LINES 53-58

.. code-block:: Python

    for f in (0.15, 0.20, 0.30, 0.40):
        moles = {"N2": f * total, "H2": (1 - f) * total}
        print(f"x(N2) = {f:.2f}: limiting reagent {limiting_reagent('N2 + H2 -> NH3', moles)}")

    plt.show()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    x(N2) = 0.15: limiting reagent N2
    x(N2) = 0.20: limiting reagent N2
    x(N2) = 0.30: limiting reagent H2
    x(N2) = 0.40: limiting reagent H2





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.819 seconds)


.. _sphx_glr_download_api_gallery_analytical_stoichiometry_plot_01_richter_stoichiometry.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_01_richter_stoichiometry.ipynb <plot_01_richter_stoichiometry.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_01_richter_stoichiometry.py <plot_01_richter_stoichiometry.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_richter_stoichiometry.zip <plot_01_richter_stoichiometry.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_